By Hui Bian

Office for Faculty Excellence

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Repeated measures ANOVA with SPSS One-way within-subjects ANOVA with SPSS

One between and one within mixed design with SPSS

Repeated measures MANOVA with SPSS

How to interpret SPSS outputs

How to report results

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When the same measurement is made several times on each subject or case, such as Same group of people are pretested and post-tested

on a dependent variable.

Comparing the same subjects under several different treatments.

Interested in the performance trends over time: is it linear, quadratic, or cubic?

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Between and within factors Between factors: a grouping or classification variables

such as sex, age, grade levels, treatment conditions etc.

Within factors: is the one with multiple measures from a group of people such as time.

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Assumptions Independence of the observations

Violation is serious

Multivariate normality Fairly robust against violation

Sphericity Not necessary for the multivariate approach

The variance-covariance matrices are the same across the cells formed by the between-subjects effects.

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A simplest design One within-subjects factor

One dependent variable

A group of subjects measured at different points in time

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Example: sample is from high school students. Research questions:

1. whether there is a significant change on frequency of drinking over time (3 months) before and after treatment;

2. whether the relationship between the within factor (time) and frequency of drinking is linear, quadratic, or cubic.

Within-subjects factor: time. Dependent variable: frequency of drinking (a28 and

b28). Two-time points data: a28 means baseline and b28

means 3-month posttest Two conditions: before treatment and after treatment

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The design

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Conditions

Subjects Before treatment After treatment

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Select Intervention group as our sample Go to Data Select Cases

Check If conditions…

Then click If

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Let Conditions = 1

Then click Continue

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Run Repeated Measures analysis Analyze General Linear Model Repeated

Measures

Type Time as Within-Subject Factor Name, type 2 as Number of Levels, then click Add

Type dv1 as Measure Name (dv means dependent variable), then click Add

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Then click Define

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After Define you should get this window

Move a28 to (1, dv1)

Move b28 to (2, dv2)

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We don’t have any between-subjects factors

Click Options to get this

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Check Compare main effects even we have two levels for within-subjects factor. I just want to show the pair comparison function.

Click Plots to get this window

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SPSS outputs Descriptive statistic results

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SPSS outputs Within-subjects effect: results of two tables are same.

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Correction options include Geenhouse-Geisser, Huyn-Feldt, and Lower-bound when sphericity is not assumed. They produce more conservative estimates.

SPSS outputs Within-subjects effect: if there is no homogeneity of

dependent variable covariance matrix, the Sphericity is not assumed. We should use the correction options.

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SPSS outputs The mathematical properties underlying the

relationship between within-subjects factor and dependent variable.

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Test linear component of Time effect

The linear component is not significant

SPSS outputs Plot

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Quadratic Cubic

SPSS outputs Pairwise comparisons: the within-subjects factor only

has two levels. So we get the same results as multivariate tests table shows.

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Results One-way within-subjects ANOVA was performed to test

whether there was a difference of frequency of drinking between before-treatment and after-treatment conditions. The observed F value was not statistically significant, F(1, 136) = .42, p = .52, partial η2 = .003, which indicated no difference of frequency of drinking over time.

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Two-way mixed design Two independent factors: one is a between-subjects

factor and one is a within-subjects factor

One dependent variable.

Tests null hypotheses about the effects of both the between-subjects factor and within-subjects factor.

Tests the effect of interactions between factors.

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Example: Research questions:

whether there is a significant change on frequency of drinking over time (3 months) between intervention and control group.

Within-subjects factor: time. Between-subjects factor: conditions (intervention vs.

control). Dependent variable: frequency of drinking (a28 and

b28). Two-time points data: a28 means baseline and b28

means 3-month posttest

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The design

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Conditions

Intervention Control

Subjects Time 1 Time 2 Time 1 Time 2

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2

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4

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Run repeated measures analysis Select all cases

Go to Analyze General Linear Model Repeated Measures

The same procedure to define the within-subjects factor and dependent variable.

Move Conditions to…

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Click Options

Click Plots

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SPSS outputs Multivariate tests

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SPSS outputs Estimated marginal means

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SPSS outputs Plots

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Results The intervention effect was analyzed using repeated

measures ANOVA. There was no statically significant difference between intervention and control group over time on frequency of drinking, F(1,285) = .90, p = .34, partial η2 = .003.

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Example Research questions:

whether there is a significant change on drinking behaviors over time (3 months) between intervention and control groups; or whether there is an intervention effect on drinking behaviors.

Within-subjects factor: time.

Between-subjects factor: conditions (two levels)

Dependent variables: frequency of drinking (a28 and b28), quantity of drinking (a31 and b31), and heavy drinking (a34 and b34).

Two-time points data: baseline and posttest

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Run repeated measures analysis

Go to Analyze General Linear Model Repeated Measures

We have three dependent variables

Still one within-subjects factor

Click Define

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Move a28/b28, a31/b31, and a34/b34 to…

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Options and Plots

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SPSS outputs Multivariate tests

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SPSS outputs Within-subjects effects

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SPSS outputs Univariate tests

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SPSS outputs Estimated marginal means

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SPSS outputs Plots: dv1 (frequency of drinking)

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SPSS outputs Plots: dv2 (quantity of drinking)

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SPSS outputs Plots: dv3 (heavy drinking)

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Results Repeated measures MANOVA test was conducted to test

intervention effect on drinking behaviors. The results showed there was no difference between intervention and control group on frequency, quantity, and heavy drinking over time, F(3, 283) = 1.18, p = .32, η2 = .01. Univariate tests also indicated there was no intervention effect on individual drinking behavior, F(1, 285) = .90, p = .34, η2 = .003 for frequency, F(1, 285) = .67, p = .41, η2 = .002 for quantity, and F(1, 285) = .39, p = .53, η2 = .001 for heavy drinking.

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Example (planned comparisons) One within-subjects factor: time

One between-subjects factor: living condition (11r)

One dependent variable: frequency of drinking (a28 and b28)

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Contrasts are used to test for differences among the levels of a between-subjects factor.

Go to Analyze General Linear Model Repeated Measures

The same procedure to define within-subjects factor and dependent variable

Click Contrasts

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You should get the left window

Choose Simple (simple means compares the mean of each level to the mean of a reference).

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Pull down

Decide which category of between-subjects factor is a reference category.

The between-subjects factor is a11r: 1= Mother and father; 2 = Mother and stepfather; 3 = Mother; 4 = Others.

Use 1 = Mother and father as a reference.

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Check First, then click Change

SPSS outputs

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Meyers, L. S., Gamst, G., & Guarino, A. J. (2006). Applied multivariate research: design and interpretation. Thousand Oaks, CA: Sage Publications, Inc.

Stevens, J. P. (2002). Applied multivariate statistics for the social sciences. Mahwah, NJ: Lawrence Erlbaum Associates, Inc.

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